On the Nearest Neighbor Rule for the Metric Traveling Salesman Problem

We present a very simple family of traveling salesman instances with $n$ cities where the nearest neighbor rule may produce a tour that is $\Theta(\log n)$ times longer than an optimum solution. Our family works for the graphic, the euclidean, and the rectilinear traveling salesman problem at the same time. It improves the so far best known lower bound in the euclidean case and proves for the first time a lower bound in the rectilinear case